No description available.

This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0<α<1, is hyperconvex. Global estimates of the exhaustion function are given. In Paper IV, it is shown that on the closure of a domain whose boundary locally is the graph of a continuous function, all plurisubharmonic functions with continuous boundary values can be uniformly approximated by smooth plurisubharmonic functions defined in neighbourhoods of the closure of the domain. Paper V studies  Poletsky’s notion of plurisubharmonicity on compact sets. It is shown that a function is plurisubharmonic on a given compact set if, and only if, it can be pointwise approximated by a decreasing sequence of smooth plurisubharmonic functions defined in neighbourhoods of the set. Paper VI introduces the notion of a P-hyperconvex domain. It is shown that in such a domain, both the Dirichlet problem with respect to functions plurisubharmonic on the closure of the domain, and the problem of approximation by smooth plurisubharmoinc functions in neighbourhoods of the closure of the domain have satisfactory answers in terms of plurisubharmonicity on the boundary.

Magistriniame darbe tiriama trisluoksnė skirtuminė schema parabolinei lygčiai su integraline sąlyga. Aprašomi metodai skaitiniai diferencialinių kraštinių uţdavinių su nelokaliosiomis sąlygomis. Atlikto magistrinio darbo rezultatas papildo iki šiol kitų mokslininkų gautus rezultatus tiriant trisluoksnę skirtuminę schemą. Magistro darbą sudaro: įvadas, uţdavinio formulavimas, 4 pagrindinės dalys, uždavinio sprendimas bei išvados. Įvadiniame skyriuje aptariamas temos aktualumas ir darbo tikslas, nurodomi naudojamo tyrimo metodai. Antrajame skyriuje suformuluojamas diferencialinis ir skirtuminis uždavinys su nelokaliąja integraline sąlyga. Trečiajame skyriuje užrašoma trisluoksnė schema kanoniniu pavidalu. Ketvirtajame skyriuje suvedame trisluoksnę schemą į dvisluoksnę. Penktajame skyriuje pateikiamas neišreikštinių skirtuminių lygčių algoritmas. Šeštajame nagrinėjama išreikštinė trisluoksnė schema bei jos algoritmas. Septintajame skyriuje tiriame matricos spektro struktūrą. Aštuntajame sprendžiamas konkretus uždavinys. Pateikiamos viso darbo bendrosios išvados. / In this master thesis there was investigated difference scheme for parabolic equation with integral condition. Numerical methods for solution differential boundary value problem nonlocal conditions methods investigated. Results of this completed work supplements by other scientists until now received results of investigation of three- layer difference scheme. Master thesis consists of introduction, problem formulation, four main chapter, numerical experiment and conclusions. Introductory chapter discusses relevance of the topic and the goal of this work, specifies methods that were used for this investigation. The second chapter formulates the differential task with nonlocal integral condition. In the third chapter is written a three- layer scheme in canonical form. In the fourth chapter the three-layer scheme reduce to the two-layers scheme. The fifth chapter presens the algorithm of realization of impicit scheme. The sixth chapter presents explicit three-layer scheme. The seventh chapter studies the structure of the matrix spectrum. There are presented all the general conclusions of the work.

Ocean environments with sloped seafloors can give rise to sound paths that do not remain in a constant plane of propagation. Numerical modelling of sound fields in such environments requires the use of computer models that fully account for out-of-plane sound propagation effects. The inclusion of these three-dimensional effects can be computationally intensive and the effects are often neglected in computer sound propagation codes. The current state-of-the art in sound propagation modelling has seen the development of models that can fully account for out-of-plane sound propagation. Such a model has been implemented in this research to provide acoustic consultants JASCO Applied Sciences with an important tool for environmental noise impact assessment in complicated marine environments. The model is described and validation results are shown for benchmark test cases. The model is also applied to study three-dimensional propagation effects in measured data from a realistic ocean environment. Particular analysis techniques assist in the interpretation of the modelled sound field for this physical test environment providing new insight into the characteristics of the test environment. / Graduate

The  aim  of  this  master  thesis  is  an  investigation  of  the  thermal  performance  of  a  thermal compound parabolic concentrating (CPC) collector from Solarus. The collector consists of two troughs with absorbers which are coated with different types of paint with  unknown  properties.  The  lower  and  upper  trough  of  the  collector  have  been  tested individually. In  order  to  accomplish  the  performance  of  the  two  collectors,  a  thorough  literature  study  in  the  fields  of  CPC  technology,  various  test  methods,  test  standards  for  solar thermal  collectors  as  well  as  the  latest  articles  relating  on  the  subject  were  carried  out. In addition, the set‐up of the thermal test rig was part of the thesis as well. The thermal  performance  was  tested  according  to  the  steady  state  test  method  as  described in the European standard 12975‐2. Furthermore, the thermal performance of  a  conventional  flat  plate  collector  was  carried  out  for  verification  of  the  test  method. The  CPC‐Thermal  collector  from  Solarus  was  tested  in  2013  and  the  results  showed  four  times  higher  values  of  the  heat  loss  coefficient  UL (8.4  W/m²K)  than  what  has been reported for a commercial collector from Solarus. This value was assumed to be too large and it was assumed that the large value was a result of the test method used that time. Therefore, another aim was the comparison of the results achieved in this work with the results from the tests performed in 2013. The results of the thermal performance showed that the optical efficiency of the lower trough of the CPC‐T collector is 77±5% and the corresponding heat loss coefficient UL 4.84±0.20  W/m²K.  The  upper  trough  achieved  an  optical  efficiency  of  75±6  %  and  a  heat loss coefficient UL of 6.45±0.27 W/m²K. The results of the heat loss coefficients  are  valid  for  temperature  intervals  between  20°C  and  80°C.  The  different  absorber paintings have a significant impact on the results, the lower trough performs overall better.  The  results  achieved  in  this  thesis  show  lower  heat  loss  coefficients UL and higher optical efficiencies compared to the results from 2013.

The present thesis is dedicated to two topics in Dynamics of Holomorphic maps. The first topic is dynamics of simple parabolic germs at the origin. The second topic is Polynomial-time Computability of Julia sets.\\ Dynamics of simple parabolic germs. Let $F$ be a germ with a simple parabolic fixed point at the origin: $F(w)=w+w^2+O(w^3).$ It is convenient to apply the change of coordinates $z=-1/w$ and consider the germ at infinity $$f(z)=-1/F(-1/z)=z+1+O(z^{-1}).$$ The dynamics of a germ $f$ can be described using Fatou coordinates. Fatou coordinates are analytic solutions of the equation $\phi(f(z))=\phi(z)+1.$ This equation has a formal solution \[\tilde\phi(z)=\text{const}+z+A\log z+\sum_{j=1}^\infty b_jz^{-j},\] where $\sum b_jz^{-j}$ is a divergent power series. Using \'Ecalle's Resurgence Theory we show that $\tilde$ can be interpreted as the asymptotic expansion of the Fatou coordinates at infinity. Moreover, the Fatou coordinates can be obtained from $\tilde \phi$ using Borel-Laplace summation. J.~\'Ecalle and S.~Voronin independently constructed a complete set of invariants of analytic conjugacy classes of germs with a parabolic fixed point. We give a new proof of validity of \'Ecalle's construction. \\ Computability of Julia sets. Informally, a compact subset of the complex plane is called \emph if it can be visualized on a computer screen with an arbitrarily high precision. One of the natural open questions of computational complexity of Julia sets is how large is the class of rational functions (in a sense of Lebesgue measure on the parameter space) whose Julia set can be computed in a polynomial time. The main result of Chapter II is the following: Theorem. Let $f$ be a rational function of degree $d\ge 2$. Assume that for each critical point $c\in J_f$ the $\omega$-limit set $\omega(c)$ does not contain either a critical point or a parabolic periodic point of $f$. Then the Julia set $J_f$ is computable in a polynomial time.

In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants. The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained. In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Sheldon Jeter; Committee Member: Sam Shelton; Committee Member: Srinivas Garimella

Thesis (Ph. D.)--University of Alabama at Birmingham, 2008. / Title from PDF title page (viewed Sept. 23, 2009). Additional advisors: Inmaculada Aban, Alexander Frenkel, Wenzhang Huang, Yanni Zeng. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.